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Explore population dynamics theory and its application to solar phenomena in this Rothschild Lecture by Professor Stanislav Molchanov. Delve into the mathematical foundations of describing particle systems with random motion and birth-death processes, examining the visible effects of irregularity and clusterization in real populations. Analyze non-linear KPP-type equations and corresponding moment equations to understand these complex systems. Discover how magnetic fields on the Sun can be modeled as an ensemble of quasi-particles, drawing parallels to population dynamics. Gain insights into the formation of sunspots as a manifestation of magnetic field intermittency, understanding how these concentrated areas of magnetic energy cover only a small portion of the Sun's surface.